Hostname: page-component-8448b6f56d-cfpbc Total loading time: 0 Render date: 2024-04-23T08:28:59.950Z Has data issue: false hasContentIssue false
  • English
  • Français

Semiprime Rings with Hypercentral Derivations

Published online by Cambridge University Press:  20 November 2018

Tsiu-Kwen Lee
Tsiu-Kwen Lee*
Affiliation:
Department of Mathematics National Taiwan University Taipei, Taiwan 10764
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let R be a semiprime ring with a derivation d, λ a left ideal of R and k, n two positive integers. Suppose that [d(xn),xn]k = 0 for all x ∊ λ. Then [λ,R]d(R) = 0. That is, there exists a central idempotent e ∊ U, the left Utumi quotient ring of R, such that d vanishes identically on eU and λ(l — e) is central in (1 — e)U

Keywords

16W2516N60semiprime ringsderivationsdifferential identities
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 4 , 01 December 1995 , pp. 445 - 449
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Beidar, K. I., Rings of quotients of semiprime rings, Vestnik Moskov. Univ. Ser I Math. Meh., (Engl, transi. Moscow Univ. Math. Bull.) 33(1978), 36–42.Google Scholar
2. Chuang, C. L., The additive subgroup generated by a polynomial, Israel J. Math. 59(1987), 98–106.Google Scholar
3. Chuang, C. L., GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103(1988), 723–728.Google Scholar
4. Chuang, C. L. and Lin, J. S., On a conjecture of Herstein, J. Algebra 126(1989), 119–138.Google Scholar
5. Chuang, C. L., Hypercentral derivations, J. Algebra 166(1994), 34–71.Google Scholar
6. Chuang, C. L. and Lee, T. K., On the one—sided version of hypercenter theorem, Chinese J. Math., to appear.Google Scholar
7. Deng, Q. and Bell, H. E., On derivations and commutativity in semiprime rings, preprint.Google Scholar
8. Felzenszwalb, B., On a result of Levitzki, Canad. Math. Bull. 21(1978), 241–242.Google Scholar
9. Herstein, I. N., Noncommutative rings, Cams Math. Monographs 15, 1968.Google Scholar
10. Kharchenko, V. K., Differential identities of semiprime rings, Algebra and Logic 17(1978), 155–168.Google Scholar
11. Lanski, C. and Montgomery, S., Lie structure of prime rings of characteristic 2, Pacific J. Math. 42(1972), 117–136.Google Scholar
12. Lanski, C. and Montgomery, S., An Engel condition with derivations, Proc. Amer. Math. Soc. 118(1993), 731–734.Google Scholar
13. Lee, P. H. and Lee, T. K., Derivations with Engel conditions on multilinear polynomials, Proc. Amer. Math. Soc, to appear.Google Scholar
14. Lee, T. K., Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica 20(1992), 27–38.Google Scholar
15. Lee, T. K., Derivations with Engel conditions on left ideals, manuscript.Google Scholar
16. Posner, E. C., Derivations in prime rings, Proc. Amer. Math. Soc. 8(1957), 1093—1100.Google Scholar
17. Rowen, L. H., Polynomial identities in ring theory, Academic Press, New York, 1980.Google Scholar
18. Vukman, J., Commuting and centralizing mappings in prime rings, Proc. Amer. Math. Soc. 109(1990), 47–52.Google Scholar